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Dynkin’s Games with Randomized Optimal Stopping Rules

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Book cover Advances in Dynamic Games

Part of the book series: Annals of the International Society of Dynamic Games ((AISDG,volume 7))

Abstract

We consider stopping games for Markov chains in the formulation introduced by Dynkin [6]. Two players observe a Markov sequence and may stop it at any stage. When the chain is stopped the game terminates and Player 1 receives from Player 2 a sum depending on the player who stopped the chain and on its current state. If the game continues infinitely, then Player 1 gets “the payoff at infinity” depending on the “limiting” behavior of the chain trajectory.

We describe the structure of solutions for a class of stopping games with a countable state space and nonnegative payoffs. The payoff is equal to zero if Player 1 stops the chain but not Player 2. These solutions require using of randomized stopping rules. We study an extent of dependence of the value for these games on the “the payoff at infinity”. It turns out that this extent is determined with the “limiting” behavior of payoffs and with the transition structure of the chain.

This study was supported by grant 01-06-80279 of the Russian Foundation of Basic Research which is gratefully acknowledged.

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Author information

Authors and Affiliations

  1. St. Petersburg Institute for Economics and Mathematics, Russian Academy of Science, St. Petersburg, Russia

    Victor Domansky

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  1. Victor Domansky
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Editors and Affiliations

  1. Institute of Mathematics, Wrocław University of Technology, Wybrzeże Wypiańskiego 27, 50-370, Wrocław, Poland

    Andrzej S. Nowak  & Krzysztof Szajowski  & 

  2. Faculty of Mathematics, Computer Science, and Econometrics, University of Zielona Góra, Podgórna 50, 65-246, Zielona Góra, Poland

    Andrzej S. Nowak

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© 2005 Birkhäuser Boston

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Domansky, V. (2005). Dynkin’s Games with Randomized Optimal Stopping Rules. In: Nowak, A.S., Szajowski, K. (eds) Advances in Dynamic Games. Annals of the International Society of Dynamic Games, vol 7. Birkhäuser Boston. https://doi.org/10.1007/0-8176-4429-6_14

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